By recognizing shapes and features of polynomial functions, sketch the graph of the function . Use a graphing utility to confirm your graph.
A)
B)
C)
D)
E)

Question

By recognizing shapes and features of polynomial functions, sketch the graph of the function  . Use a graphing utility to confirm your graph. ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The graph has two x-intercepts and two turning points, indicating a fourth-degree polynomial. The factored form of the function is (x+2)(x-1)^2(x-3). The graph must also pass through the point (0,-6), which eliminates options A and B. Option C shows only one turning point, which is incorrect. Option D has the correct number of x-intercepts and turning points but does not pass through the point (0,-6). Option E has the correct features and passes through the given point. Confirming with a graphing utility confirms our choice.

By Recognizing Shapes and Features of Polynomial Functions, Sketch the Graph